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THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 1 (2025) · pp. 419–426

DOI
10.30598/barekengvol19iss1pp419-426
ISSN
2615-3017, 1978-7227
Published
2025-01-13
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

T A torsion-free module over an integral domain is called Unique Factorization Module (UFM) if satisfied some conditions: (1) Every non-zero element has an irreducible factorization, that is, with are irreducible in and is irreducible in, and (2) if are two irreducible factorizations of, then in, and we can rearrange the order of the ’s so that in for every. The definition of UFM is a generalization of the concept of factorization on the ring which is applied to the module. In this study, we will discuss another definition that is a generalization of UFM, namely by the Weakly Unique Factorization Module (w-UFM). First, some concepts that play an important role in defining w-UFM are given. After that, the definition and characterization of w-UFM is also given. The results of this study will provide the sufficient and necessary conditions of the w-UFM.

Collaboration network of the authors

40 authors · 109 co-authorship links · showing the 40 most connected

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  • Universitas Halu Oleo
  • State University of Semarang
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Muhammad Syukri SadimantaraUniversitas Halu Oleo11
SRI REJEKIUniversitas Halu Oleo10
RH Fitri FaradillaAffiliation unknown10
Ansharullah AnsharullahUniversitas Halu Oleo8
Andi KhaeruniUniversitas Halu Oleo7
Hermanto HermantoUniversitas Halu Oleo6
Asnani AsnaniAffiliation unknown5
LA KARIMUNAUniversitas Halu Oleo4
Sigit PriatmokoState University of Semarang4
Tamrin TamrinUniversitas Halu Oleo3
Rudi HartonoAffiliation unknown3
Subiyanto Hadi SaputroAffiliation unknown3
Zuraidah ZuraidahAffiliation unknown3
Nur AsyikUniversitas Halu Oleo2
Sarinah SarinahAffiliation unknown2
Zulfa SakhiyyaAffiliation unknown2
Januarius MujiyantoAffiliation unknown2
Rahayu Puji HaryantiAffiliation unknown2
Yuni Dwi SusantiAffiliation unknown2
Abdurrachman FaridiAffiliation unknown2
Sri KadarwatiState University of Semarang2
F. ‪Widhi MahatmantiAffiliation unknown2
Harjito HarjitoAffiliation unknown2
Agung Tri PrasetyaState University of Semarang2
Jumaeri JumaeriAffiliation unknown2
Sri Wuli FitriatiAffiliation unknown2
Sri Endah WahyuningsihAffiliation unknown2
Muh Fakhrihun Na'amAffiliation unknown2
Kurnia FebiantiAffiliation unknown2
Sudawan SupriadiAffiliation unknown2
T. Mulkan SafriAffiliation unknown2
Mursyidin MursyidinAffiliation unknown2
Nurul HidayatiAffiliation unknown1
Rudi TriyonoAffiliation unknown1
Rindi Anti Nur FadhilahAffiliation unknown1
Safrika SafrikaAffiliation unknown1
Bagio BagioAffiliation unknown1
Rezqi MaliaAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
<oai_dc:dc xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/  http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
	<dc:title xml:lang="en-US">THE SUFFICIENT AND NECESSARY CONDITIONS FOR A MODULE TO BE A WEAKLY UNIQUE FACTORIZATION MODULE</dc:title>
	<dc:creator>Prabhadika, I Putu Yudi</dc:creator>
	<dc:creator>Wahyuni, Sri</dc:creator>
	<dc:description xml:lang="en-US">T A torsion-free module  &amp;nbsp;over an integral domain  &amp;nbsp;is called Unique Factorization Module (UFM) if satisfied some conditions: (1) Every non-zero element  &amp;nbsp;has an irreducible factorization, that is  , with  &amp;nbsp;are irreducible in  &amp;nbsp;and  &amp;nbsp;is irreducible in  , and (2) if  &amp;nbsp;are two irreducible factorizations of  , then  &amp;nbsp;in  , and we can rearrange the order of the  ’s so that  &amp;nbsp;in  &amp;nbsp;for every  . The definition of UFM is a generalization of the concept of factorization on the ring which is applied to the module. In this study, we will discuss another definition that is a generalization of UFM, namely by the Weakly Unique Factorization Module (w-UFM). First, some concepts that play an important role in defining w-UFM are given. After that, the definition and characterization of w-UFM is also given. The results of this study will provide the sufficient and necessary conditions of the w-UFM.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-01-13</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14036</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss1pp419-426</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application; 419-426</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss1year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14036/9609</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 I Putu Yudi Prabhadika, Sri Wahyuni</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>